Question

Grogg has drawn all of the rectangles with whole-number side lengths and an area equal to 16 square units. What is the largest possible perimeter of a rectangle that has a total number of lengths and an area of ​​16 square units?

Answer 1

`P_("Largest")=34`

Explanation:

.

If `x` is the length and `y` is the width of the rectangle then the area is:

`A=xy`

and the perimeter is:

`2x+2y`

If we keep the area `A` constant while we vary the length and width of the rectangle we will soon notice that the more we reduce the width and increase the length the larger the perimeter will get.

Theoretically, if we reduce the width to `0` the length will become `oo.`

Since we need to keep the side lengths as whole numbers, the width would have to be `1`. Then:

`A=x(1)=16`

`x=16/1=16`

`P=2(16)+2(1)=32+2=34`